Should Fractions Be Confined To The Dustbin Of Math History?
Habitually I scan the top of the morning paper, “USA TODAY – THURSDAY, JANUARY 24, 2008 – 11D”. Scan the page, let’s see…Mayan sacrifices…amphibian extinction…fractions to the DUSTBIN?! First, what is the deal with all of these articles concerning death? And second, what branch of academic pursuit has actually brought up the question, “Should fractions be consigned to dustbin of math history?” (<–???:!)
If you have ever seen a 1/1000 scale model of a ship in a jar; if you have ever measured 3/4 of a cup of flour while baking chocolate chip cookies; if you have ever given the time saying something like, “Quarter ’til Eight;” if you have ever earned 8% on an investment; if you have ever found an average; if you have ever split anything into equal groups; then you understand the value of fractions in an educated and fast-paced world. Furthermore, if you have ever studied number theory at any level then you know that to challenge the position of the fraction at any theoretical level is to challenge one of the very four primary operators and the very foundation of numbers themselves.
Fractions are a fundamental part of the study of mathematics and absolutely a necessary component to the modern day curriculum. They allow us to compare two unrelated measurements (distance divided by time – miles/hour as an example – to understand the idea of speed). Fractions are an integral part of understanding everything from rates of change to models of growth and decay. We use them in nearly every profession whether reading and understanding your electric bill in “kilowatts PER hour” or studying the proportions of the human body to create a masterpiece like Michaelangelo’s David.
In the late 1600s Gottfried Leibniz and Sir Isaac Newton showed the world that a fraction could be challenged to the very limits of its definition. Dividing by the actual value of zero we call “Undefined” as in “there is not a way to combine words, thoughts, or ideas in such a way that the human mind can conceive.” The discovery of Calculus, without a doubt, has been one of the single greatest mathematical achievements mankind has ever accomplished and it could not have been done without the concept of a fraction.
While the idea of teaching children only the decimal system appears to be wise on the outside, it robs children of gaining an early understanding of “number”. As I count to ten I begin with one digit values (i.e. 1, 2, etc) until I get to ten and then a new digit appears to the left (the tens place). This is an illustration of what its like to work in base-10 mathematics: with every group of ten I add another increment to the next place to the left.
Fractions are one of the main ideas to working in multi-base mathematics. As an example, if I am working in terms of thirds, this is like working in a base-3 system where every time I count three more I add one more to the place immediately to the next place to the left. If I am working in 7ths (base-7 i.e. days of the week), then every time I count 7 7ths I add one more to the ones place. Simple as this might seem, it is perhaps more important than ever to ensure that the modern student understands these classic fundamentals.
Dumbing down American curriculum is not the answer to the problem. We are at a point in history where we define “technology” to a large degree in terms of programming, web aps, and database management. Historically the most technologically advanced civilizations have always had an edge in global commerce and it certainly seems as if the internet will continue to be the cutting edge of technology for years to come. It really doesn’t make sense to discourage the use of fractions, and over the next few posts I will be outlining the foundation for mathematics as we know it.
– Andrew Turner
www.thinkarchimedes.com
Filed under: Commentaries, Education | Tags: Andrew Turner, Archimedes, fractions, math news
Should Fractions Be Confined To The Dustbin Of Math History?
Habitually I scan the top of the morning paper, “USA TODAY – THURSDAY, JANUARY 24, 2008 – 11D”. Scan the page, let’s see…Mayan sacrifices…amphibian extinction…fractions to the DUSTBIN?! First, what is the deal with all of these articles concerning death? And second, what branch of academic pursuit has actually brought up the question, “Should fractions be consigned to dustbin of math history?” (<–???:!)
If you have ever seen a 1/1000 scale model of a ship in a jar; if you have ever measured 3/4 of a cup of flour while baking chocolate chip cookies; if you have ever given the time saying something like, “Quarter ’til Eight;” if you have ever earned 8% on an investment; if you have ever found an average; if you have ever split anything into equal groups; then you understand the value of fractions in an educated and fast-paced world. Furthermore, if you have ever studied number theory at any level then you know that to challenge the position of the fraction at any theoretical level is to challenge one of the very four primary operators and the very foundation of numbers themselves.
Fractions are a fundamental part of the study of mathematics and absolutely a necessary component to the modern day curriculum. They allow us to compare two unrelated measurements (distance divided by time – miles/hour as an example – to understand the idea of speed). Fractions are an integral part of understanding everything from rates of change to models of growth and decay. We use them in nearly every profession whether reading and understanding your electric bill in “kilowatts PER hour” or studying the proportions of the human body to create a masterpiece like Michaelangelo’s David.
In the late 1600s Gottfried Leibniz and Sir Isaac Newton showed the world that a fraction could be challenged to the very limits of its definition. Dividing by the actual value of zero we call “Undefined” as in “there is not a way to combine words, thoughts, or ideas in such a way that the human mind can conceive.” The discovery of Calculus, without a doubt, has been one of the single greatest mathematical achievements mankind has ever accomplished and it could not have been done without the concept of a fraction.
While the idea of teaching children only the decimal system appears to be wise on the outside, it robs children of gaining an early understanding of “number”. As I count to ten I begin with one digit values (i.e. 1, 2, etc) until I get to ten and then a new digit appears to the left (the tens place). This is an illustration of what its like to work in base-10 mathematics: with every group of ten I add another increment to the next place to the left.
Fractions are one of the main ideas to working in multi-base mathematics. As an example, if I am working in terms of thirds, this is like working in a base-3 system where every time I count three more I add one more to the place immediately to the next place to the left. If I am working in 7ths (base-7 i.e. days of the week), then every time I count 7 7ths I add one more to the ones place. Simple as this might seem, it is perhaps more important than ever to ensure that the modern student understands these classic fundamentals.
Dumbing down American curriculum is not the answer to the problem. We are at a point in history where we define “technology” to a large degree in terms of programming, web aps, and database management. Historically the most technologically advanced civilizations have always had an edge in global commerce and it certainly seems as if the internet will continue to be the cutting edge of technology for years to come. It really doesn’t make sense to discourage the use of fractions, and over the next few posts I will be outlining the foundation for mathematics as we know it.
– Andrew Turner
www.thinkarchimedes.com
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